Please try to disable firewall and antivirus first, check that router/software is not blocking ports 7770, 8089, 5672, 5222, 8080, 21020-21036, 7401-7600 for the game
If this won't help, please send report through Steam Launch option "Report Connection Test" and post report name here (it will look like NAS-1234)
While we are looking into this issue re-installing the game might help as well, but that's last option after all steps which I wrote first